The chances of a mother giving birth to a son compared with a daughter are 55%-45% (This is true in the real world due to a higher male infant mortality rate although the percent might be closer together depending on the type of country. 1st world, 3rd world - more males are born than females)

In a family of four children, what are the odds a mother will have 2 boys and a girl?

Answer

I've listed all the possibilities b = boy g = girl
The chance of a child being male/female is independent, but the chance of having a certain order is just the probability multiplied by each other.
Because one child doesn't matter; the desired scenarios are any with either 3 boys 1 girl or 2 girls 2 boys.

I've marked with an X the desired outcomes, and at the end I have the probability of each occurrence.
Simply add the probabilities together for each desired case!

(as an eg of the calculation, bbgg is 0.55*0.55*0.45*0.45 which is the same answer as ggbb/ bgbg)

I know so many of you have said it, but i'll say it again. in the teaser, it was stated that there was a family of FOUR. then it was stated, and i quote, "What are the odd of being 2 boys and one girl?" 2+1=3, the odds are zero because you can never have only three kids in a family of four kids. In this situation.

Why does the phrase "2 boys" have to mean "exactly 2 boys"? If I ask, "Do you have $10?" and you look in your wallet/purse and find $30, are you going to answer yes or no? I would say yes. Ergo: I think the answer to the problem is correct.

I think some people need to go study some probability before commenting on these teasers. Four children, with two boys and one girl means that there are two possible scenarios that fit. Either there are two boys and two girls, or there are three boys and a girl. Both situations satisfy the criterion of there being two boys and a girl. The fourth child can be either a boy or a girl.

snaps is right. the open ended "2 boys and 1 girl" is quite common with probability problems. it's implied that the fourth child can be either. by complaining that it doesn't explicitly state the two cases is to illustrate one's lack of experience with mathematics and statistics.

I disagree with the solution. You do not suspend common English in describing problems just because it is Mathematics. This is like a riddle "What has 2 legs and a long neck Answer: A giraffe, I didn't tell you about the other 2 legs." This might be fine as a joke but if you say there are 2 boys and a girl in the family you at least have to say at least!!! if you'll excuse the pun. 2 boys and a girl means 3 children. Those people who are arguing otherwise speak a different language to me. When you meet an old friend and ask if they have any children and they say 2 boys and a girl, then your normal reply would be "But how many children have you got?" or "What are the other ones then?" I don't think so!